Context. Bright Fe-Kα line emission at 6.4 keV is a unique characteristic of some of the dense molecular complexes present in the Galactic center region. Whether this X-ray fluorescence is due largely to the irradiation of the clouds by X-ray photons or is, at least in part, the result of cosmic-ray particle bombardment, remains an interesting open question. Aims: We present the results of XMM-Newton observations performed over the last eight years of the region surrounding the Arches cluster in the Galactic center. We study the spatial distribution and temporal behaviour of the Fe-Kα emission with the objective of identifying the likely source of the excitation. Methods: We have constructed an Fe-Kα fluence map in a narrow energy band of width 128 eV centered on 6.4 keV. We use this to localize the brightest fluorescence features in the vicinity of the Arches cluster. We have investigated the variability of the 6.4-keV line emission of several clouds through spectral fitting of the EPIC MOS data with the use of a modelled background, which avoids many of the systematics inherent in local background subtraction. We also employ spectral stacking of both EPIC PN and MOS data to search for evidence of an Fe-K edge feature imprinted on the underlying X-ray continuum. Results: The lightcurves of the Fe-Kα line emission from three bright molecular knots close to the Arches cluster were found to be constant over the 8-year observation window. However, West of the cluster, we found a bright cloud which shows the fastest Fe-Kα variability yet seen in a molecular cloud in the Galactic center region. The time averaged spectra of the molecular clouds revealed no convincing evidence of the 7.1-keV edge feature, albeit with only weak constraints. The EW of the 6.4-keV line emitted by the clouds near to the cluster was found to be ~1.0 keV. Conclusions: The observed Fe-Kα line flux and the high value of the EW suggest an origin of the fluorescence in the photoionization of the MCs by X-ray photons, although excitation by cosmic-ray particles is not specifically excluded. For the three clouds nearest to the Arches cluster, the identification of the source of these X-rays as an earlier outburst on Sgr A* is at best tentative, although not entirely ruled out by the observations. On the other hand, the hardness of the nonthermal component associated with the 6.4-keV line emission might be best explained in terms of the bombardment of the clouds by cosmic-ray particles emanating from the Arches cluster itself. The relatively short-timescale variability seen in the 6.4-keV line emission from the cloud to the west of the cluster is most likely the result of its X-ray illumination by a nearby transient X-ray source.